Social, Behavioral & Experimental Economics (SBEE): A Theory of Multiplexity: Sustaining Cooperation with Multiple Relationships

Abstract
People are embedded in multiple social relations. These relationships are not isolated from each other: the network pattern of an existing relationship is likely to affect the formation of a new relationship. This paper provides a framework to analyze the multiplex of networks. We present a model in which each pair of agents may form more than one relationship. Each relationship/link is captured by an infinitely repeated prisoner’s dilemma, with endogenous stake of cooperation. We show that multiplexity, i.e. having more than one relationship on a link, boosters incentives as different relationships serve as social collateral for each other. We then endogenize the network formation and ask: when an agent has a new link to add, will she multiplex with a current neighbor, or link with a stranger? We find the following: (1) There is a strong tendency to multiplex, and “multiplexity trap” can occur. That is, agents may keep adding relationships with current neighbor(s), even if it is more compatible to cooperate with a stranger. (2) Individuals tend to multiplex when the current network (a) has a low degree dispersion (i.e., all individuals have similar numbers of friends), or (b) is positively assortative (homophily in degree). We also provide empirical evidence that is consistent with our theoretical findings.